# Eisenstein prime

Given the complex cubic root of unity $\omega=e^{{2i\pi}\over{3}}$, an Eisenstein integer $a\omega+b$ (where $a$ and $b$ are natural integers) is said to be an Eisenstein prime if its only divisors are 1, $\omega$, $1+\omega$ and itself.

Eisenstein primes of the form $0\omega+b$ are ordinary natural primes $p\equiv 2\mod 3$. Therefore no Mersenne prime is also an Eisenstein prime.

Title Eisenstein prime EisensteinPrime 2013-03-22 16:10:10 2013-03-22 16:10:10 PrimeFan (13766) PrimeFan (13766) 6 PrimeFan (13766) Definition msc 11R04 EisensteinIntegers